Econometric Theory



MISCELLANEA

BAYESIAN CONSISTENCY FOR STATIONARY MODELS


Antonio  Lijoi  a1 , Igor  Prünster  a2 and Stephen G.  Walker  a3 c1
a1 University of Pavia and CNR-IMATI Milan
a2 University of Turin College Carlo Alberto, and ICER
a3 University of Kent

Article author query
lijoi a   [Google Scholar] 
prunster i   [Google Scholar] 
walker sg   [Google Scholar] 
 

Abstract

In this paper, we provide a Doob-style consistency theorem for stationary models. Many applications involving Bayesian inference deal with non independent and identically distributed data, in particular, with stationary data. However, for such models, there is still a theoretical gap to be filled regarding the asymptotic properties of Bayesian procedures. The primary goal to be achieved is establishing consistency of the sequence of posterior distributions. Here we provide an answer to the problem. Bayesian methods have recently gained growing popularity in economic modeling, thus implying the timeliness of the present paper. Indeed, we secure Bayesian procedures against possible inconsistencies. No results of such a generality are known up to now. a


Correspondence:
c1 Address correspondence to Stephen G. Walker, Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Kent CT2 7NZ, UK; e-mail: S.G.Walker@kent.ac.uk


Footnotes

a The authors are grateful for the comments and suggestions of two referees. Antonio Lijoi and Igor Prünster were supported by the Italian Ministry of University and Research, grants 2006134525 and 2006133449, respectively. The research of Stephen G. Walker was funded by an EPSRC Advanced Research Fellowship.



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